A Study On Key Problems For Face Recognition

Feature extraction is a key problem in the study of face recognition. Face images obtained by image acquisition equipment construct the high-dimensional face observation space, and discriminative features of human face lie on the low manifold (subspace) formed by face samples. What is the feature extraction is the process of searching the low-dimensional discriminative subspace (manifold) from the high-dimensional observation space. During this process, illumination processing and dimensionality reduction is the two crucial steps. The distribution of face sample data in the observation space is sparse essentially, while that of each class is highly overlapping with each other, resulting that the differences of face samples within classes are larger than that between classes. Processing the illumination of face images effectively can adjust the distribution form of face samples in the observation space, reducing the differences within classes, increasing those between classes, and thus laying a good foundation for the followed dimensionality reduction (feature extraction). However, face images, after handling lighting, still stay in the observation space, and the high-dimensional property of vectors will incur’Curse of Dimensionality’ and ’measure concentration’, in which case it is hard to achieve good results by using classifiers to classify the samples directly. Therefore, it becomes the central task in the study of face recognition how to design effective algorithms of reducing dimensionality to extract the low-dimensional face features from the high-dimensional observation space with the most powerful discriminative. Followed this idea, we made an intensive study on these two crucial steps of processing illumination and extracting features from the view of theory and technology, and proposed some new idea and solutions based on the existing research results.The kernels of Gabor wavelet are similar to the response of the two-dimensional receptive field profiles of the mammalian simple cortical cell, and exhibit the desirable characteristics of capturing salient visual properties such as spatial localization, orientation selectivity, and spatial frequency selectivity. Therefore, the Gabor features of images are insensitive to the variations of illumination, pose and expression. Based on this property of Gabor wavelet, we first made a Gabor transform to face images, with the facial Gabor features obtained; and then proposed a locality preserving based supervised manifold learning algorithm designed for the high-dimensional Gabor features, called Supervised Neighborhood Preserving Embedding, by which the dimensionality is reduced effectively. Experimental results on the two face databases of Yale and ORL show the feasibility of the proposed algorithm.Similar to the Gabor wavelet, Nonsubsampled Contourlet Transform (NSCT) is also a multi-scale and multi-direction2D wavelet transform. The difference from the Gabor wavelet is that the basis functions of NSCT is orthogonal to each other, with the least redundant information contained by the sub-bands of NSCT. In consideration of this good feature of NSCT, we transformed, based on the Retinex illumination model, the face image into NSCT domain, used adaptive threshold to filter each high-frequency sub-band, and obtained the illumination invariant of face images by using inverse NSCT. Experimental results indicated that the proposed algorithm can very effectively reduce the effect of illumination variation on face images, improving the recognition rate of the algorithm to a large extent.Manifold learning has a core idea of preserving the local geometric properties of the data space during the process of reducing the dimensionality, which is now a mainstream nonlinear subspace method and wildly applied to face recognition. In this paper, according to the distribution feature of face samples, we proposed3kinds of supervised learning algorithms for face recognition based on an analysis of limits of some manifold learning algorithms.(1) Adaptive Supervised Locality Optimal Preserving Projection (ASLOPP). After investigating some drawbacks of existing supervised LPP algorithms in classification problem, ASLOPP method determines the neighborhood size of each data in sample space by using adaptive neighborhood algorithm, adds constraint conditions, and employs iterative method to optimize the objective function, which leads to orthogonal basis vectors in low-dimensional embedding, decreasing the information redundancy in the embedding while increasing the discriminative power. We conducted experiments on Extended Yale B and CMU PIE face databases, with good results improving the face recognition rates obviously.(2) Supervised Locality Preserving Projection (SLPP). This algorithm is also based on LPP, which first employs adaptive neighborhood method for determining the sample neighborhood size in the process of constructing the eigenmap of sample space, in terms of the distribution of facial feature space. Then the prior class label information of samples is used to construct within-class and between-class maps, respectively, by which the distribution of each class is represented. And the objective function absorbs the idea of LDA, which allows the optimized embedding not only maintain the local geometry of the original sample space, but also minimize the within-class variance while maximize the between-class one, greatly enhancing the discriminative of the embedding.(3) Supervised Neighborhood Preserving Embedding. On the basis of the Neighborhood Preserving Embedding (NPE), this algorithm determines the link mode between samples by the class label in constructing the neighborhood map of the sample space. By optimization of the objective function, the embedding holds the local linearity of the sample space optimally, and also greatly improve the discriminative power.